Endoprostheses are known (EP-B 474 015) whose components are connected to one another via a cone connection. The latter comprises a conical bore on one component and a conical plug on the other component, the conical plug matching the conical bore and being received by it. When a sufficiently small cone angle is chosen, these fit securely one within the other, as long as they have been joined together with sufficient force at the time of assembly. To safeguard it against chance damage, this cone connection is provided with a securing screw which sits in a threaded bore of one component and can be screwed forwards with its tip into a corresponding recess in the other component transverse to the direction of release. In the event of follow-up surgery, the securing screw is not readily accessible. The removal of the prosthesis which is to be replaced is thus made difficult.